Using Holevo bound for leakage estimation in quantum key distribution

Abstract

Side-channel imperfections in quantum key distribution (QKD) are often treated within the GLLP and Koashi framework, which typically produces overly conservative key-rate estimates. Conditional-entropy approaches based on the Holevo bound provide a less pessimistic alternative but must correctly account for post-selective measurements, such as unambiguous state discrimination. We show that general post-selective soft-filtering transformations of side-channel states can be consistently incorporated into this framework. By relating the distinguishability of filtered Trojan-horse-attack states to observable parameters, namely, the reflected mean photon number and the single-photon yield, we derive a Holevo-based upper bound on the eavesdropper's information for decoy-state BB84. Numerical comparison demonstrates that this method yields significantly higher key rates than the GLLP and Koashi approach when the side-channel intensity is large, extending the secure distance by tens of kilometers. This provides a practical and tighter tool for leakage estimation in modern QKD systems.